The dispersion generalized Benjamin-Ono equation
| Autor: | Ai, Albert, Liu, Grace |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We consider the well-posedness of the family of dispersion generalized Benjamin-Ono equations. Earlier work of Herr-Ionescu-Kenig-Koch established well-posedness with data in $L^2$, by using a discretized gauge transform in the setting of Bourgain spaces. In this article, we remain in the simpler functional setting of Sobolev spaces, and instead combine a pseudodifferential gauge transform, a paradifferential normal form, and a variable coefficient Strichartz analysis to establish well-posedness in negative-exponent Sobolev spaces. Our result coincides with the classical well-posedness results obtained at the Benjamin-Ono and KdV endpoints. Comment: 40 pages |
| Databáze: | arXiv |
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